An Efficient Adaptive Mesh Redistribution Method for Nonlinear Eigenvalue Problems in Bose-Einstein Condensates

摘要

We design a multilevel correction type of adaptive finite element method based on the moving mesh technique for solving nonlinear eigenvalue problems. In this paper, we take the ground state of Bose-Einstein condensates as the example of a nonlinear eigenvalue problem to show the solving process. For this aim, we propose a non-nested augmented subspace method for the nonlinear eigenvalue problems since the sequence of finite element spaces generated by the r-adaptive method has non-nested property. The new method proposed in this paper can improve the efficiency for solving nonlinear eigenvalue problems by the corresponding theoretical analysis and numerical examples.

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